Supporters of the Senate's Iran legislation know they have to do a delicate dance on the floor.

With Majority Leader Mitch McConnell, R-Ky., promising an open-amendment process for the bill negotiated by Foreign Relations Chairman Bob Corker, R-Tenn., and ranking Democrat Benjamin L. Cardin of Maryland, the advocates for the carefully crafted compromise know they will have to bat back unwanted amendments — including some they might support — to stave off the return of a veto threat from President Barack Obama.

"The White House has made very plain that they dropped their veto threat for the bill as constituted," Sen. Tim Kaine, D-Va., said. "Look, I was one of the co-sponsors, but there might be amendments that would cause me to withdraw. If there are amendments that try to take what has been scrupulously nonpartisan and make it partisan, you're going to see a lot of people who are on the bill moving off of it."

Kaine also expressed confidence that members of the Foreign Relations Committee who shepherded its 19-0 panel vote would work to keep it on a "nonpartisan track" through the chamber, and Cardin said he and Corker are committed to defeating any "poison pill" amendments. The measure has 62 co-sponsors.

To Kaine's point, Minority Whip Richard J. Durbin, D-Ill., said the addition of contentious language could very easily keep the measure from even getting out of the Senate.

"We have a solid, bipartisan bill supported by the White House. If it is diverted from that path to passage with divisive amendments, there's no guarantee," Durbin said.

Sen. Lindsey Graham, a fellow supporter of the package, went a step further.

"Anybody who offers an amendment that will break this agreement apart that I think is solid foundationally, the beneficiary will be the Iranians. I hope you understand this," the South Carolina Republican said.

There was no shortage of amendments filed even before the Senate adjourned for the week, including by other 2016 GOP presidential hopefuls.

For instance, Sen. Ted Cruz, R-Texas, has drafted an amendment with Republican Patrick J. Toomey of Pennsylvania designed to require lawmakers to approve any final deal reached with Tehran, rather than establish a process for expressing disapproval, as currently drafted.

"The amendment is designed to put the power where it should be: in the hands of Congress," Cruz spokeswoman Amanda Carpenter said in a statement. "The President should be required to receive affirmative congressional approval of any Iran deal, rather putting the onus on Congress to stop it."

Florida Sen. Marco Rubio has already filed seven amendments, some with the backing of Republican colleagues. They include a proposal to require certification that Iran has recognized Israel's right to exist as a Jewish state and another to require certification that the Iranian government has released all detained Americans.

Neither of those are certifications Obama would likely be able to make, and critics of such requirements say they fall outside the scope of the current talks with Iran.

Sen. Mark S. Kirk, R-Ill., joined Rubio on each of those amendments, and the two senators also came together in issuing an April 20 statement about Iran's pursuing espionage charges against Jason Rezaian of The Washington Post.

"This case is just the latest example of the true nature of the Iranian regime. The Obama Administration should demand Mr. Rezaian's immediate release along with all other Americans wrongfully imprisoned in Iran prior to concluding a nuclear deal with this brutal regime," Kirk and Rubio said.

Other amendments that have already been filed include a pair of proposals from Sen. Ron Johnson that have similar intents. The Wisconsin Republican wants any final product of the negotiations with the Iranians to be treated either as a congressional-executive agreement with expedited procedures for consideration or as a formal treaty.

The panel's former ranking member, Sen. Robert Menendez, D-N.J., came out strongly for the deal. "In my view, the best way to send a clear message to Tehran about our expectations is for Congress to pass the [bill] as it was voted out of committee," Menendez said in opening floor debate. "The spirit of bipartisanship that underscores Congress' critical role in the highest priority, national security, nuclear-nonproliferation challenge of our time was unanimously proposed in the Foreign Relations Committee, and I hope we can send the same message from the floor of the Senate."

And in a message that seems designed for Republicans, Corker is already warning that the alternative to the legislation he put together with Cardin, Menendez and others, would be to grant all ultimate authority to Obama.

"Without this bill, there is nothing stopping the president from bypassing the American people, immediately waiving sanctions imposed by Congress and unilaterally implementing an agreement with Iran," Corker said. "This legislation ensures the president will submit an agreement to Congress for review and a vote."